543

HISTORY OF PHYSICAL ASTRONOMY.

the quantity of light emitted by it relative to any other star whose placeis assigned in the scale ; and it is contradictory, inasmuch as in number-less instances the same star has a different magnitude assigned to it bydifferent authorities. Bailty proposed to amend the system of stellarnomenclature by determining the brightness of each star upon strict photo-metrical principles. To this end he suggested that all the stars shouldbe observed with the same telescope, and that in every instance the aper-ture should be diminished until the star just ceased to be visible*. It isobvious that the light usually emitted by any star to the earth would thenbe inversely proportional to the corresponding aperture. This mode ofdetermining the relative brightness of the stars is unexceptionable inpoint of theory, but practical difficulties have hitherto stood in the way ofits adoption as the basis of a new system of nomenclature.

Sir William Herschel rejected the system of magnitudes altogether, asunworthy of any reliance, and determined the relative brightness of a greatnumber of stars visible to the naked eye, by comparing each star with theother stars in its vicinity, and noting those which were sensibly equal toit in lustre, or differed from it only in a very small degree. The resultsof his labours on this occasion form a valuable record for ascertaining atsome future epoch whether any of the stars to which they refer haveundergone a variation of lustre f.

More recently Sir John Herschel has employed a similar method inconnecting a great number of stars distributed over both hemispheres inone unbroken chain of relative brightness, and has also succeeded inadapting the results to the conventional system of magnitudes so as torepresent the brightness of the various stars according to the usualnomenclature, but in a vastly-improved condition as respects accuracy ofdetail. The same distinguished astronomer has moreover determined, bya series of photometrical experiments, the quantity of light actuallyemitted by each star relative to a certain standard star considered asthe unit of light, and has instituted a comparison between the resultsand the corresponding magnitudes of the stars. The conclusion to whichhe was conducted by his researches on this occasion, is at once curiousand instructive. It appeared that if the conventional magnitudes of thestars as rectified by him, were all increased by the common fraction 0-414,the squares of the resulting magnitudes would then be inversely pro-portional to the corresponding photometric numbers, representing thelight of the stars as determined by experiment. Now this is preciselythe relation that would subsist between the distances of the stars from theearth, and their respective photometric intensities, on the probable sup-position that they all yield the same quantity of light at the same distance.It follows, therefore, that the ordinary nomenclature of magnitudes, whensufficiently amended, represents pretty nearly the order of the distancesof tire stars, and would even rigorously do so, provided the magnitudeswere augmented by the common fraction above mentioned J. An examplewill illustrate this curious conclusion more clearly. The bright star aCentauri being assumed as the standard unit in the scale of conventionalmagnitudes, the star Antares, according to Sir John Herschel , will berepresented in the same scale by 1-6. Now if the distance of a. Centauri

* Mem. Acad, des Sciences, 1771, p. 580.

t See Phil. Trans., 1796, 1797, 1799.

t Results of Ast. Observ., &c., p. 304, et seq.